The strange magnetic form factor of the nucleon is studied in a chiral effective model motivated by the heavy baryon formalism at next-to-leading order. The one-loop contributions from kaon and intermediate octet and decuplet hyperons are included, using finite-range regularization to deal with the ultraviolet divergences. Drawing on an established connection between quenched and full QCD, this model makes it possible to predict the strange magnetic form factor under the hypothesis that for a dipole regulator mass. around 0.8 GeV, strangeness in the core is negligible. The strange magnetic form factor is found to be small and negative over a range of momentum transfer, while the strange magnetic moment is consistent with the best lattice QCD determinations.